Although the injury was not causing the 24-year-old any pain, medical staff decided an operation was necessary to repair the damage and the recovery period will be at least three months.
Rokocoko told the Blues' website: "It's hard for me to leave the team and not play, especially when my wrist doesn't really hurt.
"But I'm in the hands of the medical staff and the long-term risks outweigh any option to keep on playing for the short term."
The news is another blow for the Blues, who suffered narrow defeats in their last two home games and have lost three of their last five in total.
Coach David Nucifora added: "Joe is a much-valued team-mate in our squad. His contribution on and off the field for the Blues this season has been tremendous and we will certainly miss him from our ranks.
"Post surgery Joe will continue to play a support role within our squad and we will be doing all we can to assist with his recovery."